A Free-Space Measurement Method for the Low-Loss Dielectric Characterization Without Prior Need for Sample Thickness Data

Abstract

A free-space measurement method is presented for the characterization of low-loss dielectric materials at millimeter-wave frequencies that does not require any assumption of <i>a priori</i> knowledge of the sample thickness. The method first employs only maximal and minimal envelopes of measured transmission scattering parameters to determine the real part <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>ε</mml:mi> <mml:mi>r</mml:mi> <mml:mo>'</mml:mo></mml:msubsup> </mml:mrow> </mml:math> of the permittivity of test materials. Subsequently, the thickness of the sample is estimated from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>ε</mml:mi> <mml:mi>r</mml:mi> <mml:mo>'</mml:mo></mml:msubsup> </mml:mrow> </mml:math> and frequencies for maximal and minimal peaks of the transmission scattering parameter. The calculation of the imaginary part <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msubsup><mml:mi>ε</mml:mi> <mml:mi>r</mml:mi> <mml:mrow><mml:mo>″</mml:mo></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> of the permittivity then easily follows. Our method is examined by measuring two cross-linked polystyrene samples, one polytetrafluoroethylene sample and one polymethylpentene sample in the frequency range of 220-325 GHz at the incident angles of 0°, 10°, 20°, and 30°. Moreover, an explicit uncertainty analysis for the permittivity is derived, and uncertainties of the extracted complex permittivity are reported.